Bethe Ansatz and Classical Hirota Equation

Details Bethe Ansatz and Classical Hirota Equation Bethe Ansatz and Classical Hirota Equation

1996-10-16

arxiv.org/abs/cond-mat/9610132v1

Int.J.Mod.Phys. B11 (1997) 75

Physics

Condensed Matter

Statistical Mechanics

15 pages, Latex, special World Scientific macros included

Scientific paper

10.1142/S0217979297000101

We discuss an interrelation between quantum integrable models and classical soliton equations with discretized time. It appeared that spectral characteristics of quantum integrable systems may be obtained from entirely classical set up. Namely, the eigenvalues of the quantum transfer matrix and the scattering $S$-matrix itself are identified with a certain $\tau$-functions of the discrete Liouville equation. The Bethe ansatz equations are obtained as dynamics of zeros. For comparison we also present the Bethe ansatz equations for elliptic solutions of the classical discrete Sine-Gordon equation. The paper is based on the recent study of classical integrable structures in quantum integrable systems, hep-th/9604080.

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